Quantification of ventilation characteristics of a helmet

ARTICLE IN PRESS Applied Ergonomics 39 (2008) 332–341 www.elsevier.com/locate/apergo Quantification of ventilation characteristics of a helmet A. Van Brecht, D. Nuyttens, J.M. Aerts, S. Quanten, G. De Bruyne, D. Berckmans Measure, Model and Manage Bioresponses, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium Received 20 April 2004; accepted 30 August 2007 Abstract Despite the augmented safety offered by wearing a cyclist crash helmet, many cyclists still refuse to wear one because of the thermal discomfort that comes along with wearing it. In this paper, a method is described that quantifies the ventilation characteristics of a helmet using tracer gas experiments. A Data-Based Mechanistic model was applied to provide a physically meaningful description of the dominant internal dynamics of mass transfer in the imperfectly mixed fluid under the helmet. By using a physical mass balance, the local ventilation efficiency could be described by using a single input–single output system. Using this approach, ventilation efficiency ranging from 0.06 volume refreshments per second (s1) at the side of the helmet to 0.22 s1 at the rear ventilation opening were found on the investigated helmet. The zones at the side were poorly ventilated. The influence of the angle of inclination on ventilation efficiency was dependent on the position between head and helmet. General comfort of the helmet can be improved by increasing the ventilation efficiency of fresh air at the problem zones. r 2007 Elsevier Ltd. All rights reserved. Keywords: Tracer gas; Grey box model; Ventilation efficiency 1. Introduction In professional cycling, a lot of racing cyclists complain about the fact that riding with a helmet is uncomfortable due to high temperatures and sweating under the helmet. In countries where the helmet is not obligatory (e.g. France), the majority of the amateur cyclists refuse to wear the helmet especially in the mountain stages during hot summer days. The discomfort of high temperatures and moisture concentrations around the head of the cyclist when wearing the crash helmet is the main reason for not wearing one (Wardle and Iqbal, 1998). The amount of heat released by the human head is under normal conditions 40–50% of the total heat production of the body and increases with increasing activity level (Rasch et al., 1991). The combination of the high heat production of the head and the insufficient ventilation efficiency of the helmet lead to uncomfortable gradients in temperature and moisture between head and helmet. Furthermore, the Corresponding author. E-mail address: Daniel.Berckmans@biw.kuleuven.be (D. Berckmans). 0003-6870/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.apergo.2007.08.003 thermal balance of the head has a great influence on the complete human body. Experiments showed that cooling of the head significantly decreases the heart rate, the internal body temperature and skin temperature values on other body parts (Ku, 1999). Wearing a helmet reduces the chance of severe head injury significantly. In USA, yearly 500,000 cyclists get head injuries in traffic accidents, although 50% of them could be avoided by wearing a helmet (Edmund, 1988; Cherington, 2000). Therefore, it is of major importance to improve the thermal features underneath a crash helmet in order to increase people’s motivation to wear one, and thus to reduce drastically the head injuries among cyclists. Computational Fluid Dynamics (CFD) offers bright prospects as a tool for the design and optimisation where fluid flow phenomena play a major role. Although CFD can be applied successfully to model velocity, temperature distributions to a high level of detail, it must be used with care. One must be aware of the fact that a CFD model constitutes the culmination of a large number of assumptions and approximations, such that the produced output ARTICLE IN PRESS A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 has limited accuracy. The use of an insufficiently dense grid, the selection of an improper turbulence model and carelessly specified boundary conditions can lead to erroneous results. The engineer who wishes to use CFD to assist in system design needs to be fully aware of these ‘two edges of the CFD-sword’ (Baker et al., 1997). It is also surprising that throughout the literature few attention is paid to the validation of CFD computations. The objective of this research was to quantify the ventilation characteristics of a helmet by using a DataBased Mechanistic (DBM) modelling approach as a tool for evaluating the ability of a helmet to remove heat and moisture. DBM, a hybrid approach between the extremes of mechanistic and data-based modelling which provides a physically meaningful description of the dominant internal dynamics of mass transfer in the imperfectly mixed fluid (Berckmans, 1986) is proposed (Berckmans et al., 1992a; Janssens et al., 2003). This approach has the advantage that the model structure of a DBM model provides a physically meaningful description of the process dynamics (Van Brecht et al., 2002; Janssens et al., 2003), yields information on the air quality between head and helmet and this in combination with a high accuracy. This DBM approach is not only applicable for helmets for cyclists, but also for evaluating the ventilation characteristics of safety helmets, crash helmets and American football helmets. 333 quantify the fresh air concentrations and characterising the flow field (Sandberg and Blomqvist, 1985). The ideal tracer gas has a density equal to the density of air, its concentration is easy to measure, it is not inflammable, toxic nor explosive, it is in normal circumstances not present in the air, does not decay and is inert. Unfortunately, no gas satisfies all these properties. In the experiments, CO2 was chosen as a tracer gas because its properties approximate the ideal gas. Since the measurements were carried out in a large well-ventilated room, the CO2 concentration in the room can be assumed nearly constant. A pressurised gas bottle used in this study contained a mixture of 99% CO2 in N2 and a computer controlled solenoid valve controlled the injection of CO2 into the air stream through the fan. The CO2 concentration of the air at the nine different sampling positions was measured by a gas analyser (Rosemount Binos 100 2M) (Fig. 2). A pump and multiplexer was placed between measurement point and the gas analyser. A pump sucked the air from the measurement point to the gas analyser. The multiplexer chooses the channel that was recorded, so the nine channels are measured after each other (Fig. 3). Each measurement setup was repeated 10 times to assure statistical significance for each response. The mannequin head was positioned on a stand with controllable tilting 2. Materials and method 4 2.1. Test installation 2 3 To quantify the ventilation characteristics of a helmet, a helmet for cyclists was placed on a manikin head (Fig. 1). Further, nine sampling positions were defined, located only in the right half of the helmet, since symmetry was assumed (Fig. 1). To quantify the indoor air quality, tracer gases are widely used as reported in literature (Roulet and Vandaele, 1991). The tracer gas technique is described as a method to 5 1 6 Fig. 2. Schematic representation of the test installation. (1) Pressurised CO2 gas bottle, (2) solenoid valve, (3) ventilator with injection point of CO2, (4) sampling of the tracer gas in the helmet, (5) pump, (6) CO2 analyser. Front 1 6 3. 2 3 4 2. 8 Shock absorbing material 7 9 Ventilation openings 4. 7 9 6. 1. 5. 8. 5 Rear Fig. 1. Schematic representation of the manikin head with wig and the nine sampling positions, between the head and the helmet, of tracer gas concentration in the helmet. ARTICLE IN PRESS 334 A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 DATA Estimation of the model structure and parameters Mechanistic formulation of the model structure Data-based phase Mechanistic phase Fig. 3. The DBM modelling approach. and height. The helmet was positioned according to EU safety standards. The head was tilted forward with 301 at a distance of 50 cm from the air inlet. discrete-time TF models and not on their continuous-time model equivalents, which impedes the interpretation of the model in physically meaningful terms. Although Least Squares (LS) is one of the most commonly used model estimation algorithms, the estimated model parameters become asymptotically biased away from their true values in the presence of measurement or disturbance noise (Young, 1984). The more complex Simplified Refined Instrumental Variable (SRIV) algorithm, developed by Young (1984), uses the Instrumental Variable (IV) approach coupled with special adaptive prefiltering to avoid this bias and to achieve good estimation performance. The SRIV structure identification criterion has been proven very successful in practical applications (Young and Jakeman, 1979, 1980; Quanten et al., 2003). A continuous-time TF model for a single input–single output (SISO) system has the following general form: yðtÞ ¼ 2.2. Data-Based Mechanistic models As illustrated in Fig. 3, the DBM approach consists of two phases: a mechanistic and a data-based phase. In the data-based phase, experimental data are exploited to estimate the most appropriate model structure and associated model parameters. In the mechanistic phase, a model structure is formulated based on physical knowledge and assumptions about the physical nature of the process and in agreement with the model structure estimated in the data-based phase. Generally, the DBM approach applied to mixing processes represents the imperfectly mixed fluid in a process by a number of Well-Mixed Zones (WMZ) which are defined around the nodes of a sensor grid. A WellMixed Zone is a zone of improved mixing with a certain volume wherein acceptable low spatial gradients occur (Fig. 4). The kind of spatial gradients, and consequently the acceptable values and thus the number of WMZ, are dependent on the application, in this case the gradients in gas concentration under a crash helmet. Examples of a DBM approach can be found in Janssens et al. (2003), Quanten et al. (2003), Van Brecht et al. (2005) and Zerihun Desta et al. (2005). In DBM models, the model structure is first identified using objective methods of time-series analysis based on a given, general class of time-series model (here linear, continuous-time transfer functions (TF) or the equivalent ordinary differential equations). But the resulting model is only considered fully acceptable if, in addition to explaining the data well, it also provides a description that has relevance to the physical reality of the system under study. 2.2.1. Identification of a reduced-order, linear model The parameters of a TF model may be estimated using various methods of identification and estimation (Ljung and Soderstrom, 1983; Young, 1984; Norton, 1986; Ljung, 1987). However, most of these methods are based on BðsÞ uðt  tÞ þ xðtÞ, AðsÞ (1) where s is the time derivative operator, i.e. s ¼ d/dt; y(t) is the noisy measured output (in this case the CO2 concentration measured under the helmet); u(t) is the model input (in this case the CO2 concentration emitted at the fan); t is the time delay; x(t) is additive noise, assumed to be a zero mean, serially uncorrelated sequence of random variables with variance s2 accounting for measurement noise, modelling errors and effects of unmeasured inputs to the process; and finally, A(s) and B(s) are polynomials in the s operator of the following form: AðsÞ ¼ sn þ a1 sn1 þ    þ an BðsÞ ¼ b0 sm þ b1 sm1 þ    þ bm ð2Þ where mpn; a1, a2, y, an and b0, b1, y, bm are the TF denominator and numerator parameters, respectively. The ability to estimate the parameters of a TF model represents only one side of the model identification problem. Equally important is the problem of objective model order identification. This involves the identification of the best choice of orders n and m of the TF polynomials A(s) and B(s) and of the time delay t. The process of model order identification can be assisted by the use of wellchosen statistical measures which indicate the presence of overparameterisation. A possible identification procedure is the Akaike’s Information Criterion (AIC; Akaike, 1973). AIC takes the weighted sum of model accuracy (R2) and model compactness (simple model structure with a minimal number of model parameters) into account. A refined procedure is the Young Identification Criterion (YIC). This procedure takes the model accuracy, model compactness plus the parametric efficiency into account (the parametric efficiency is the reliability of the parameter estimation expressed through the standard deviation on the parameters estimation). As in AIC, the model that minimises the YIC provides a good compromise between goodnessof-fit, compactness and parametric efficiency. We identified ARTICLE IN PRESS A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 335 Fig. 4. The concept of Well-Mixed Zones (WMZ). Each zone is defined by its volume and an acceptable range of ventilation efficiency. These zones vary in time. the most appropriate model structure [n, m, t] based on the minimisation of the YIC: ! ! np 1X s^ 2 s^ 2 p^ ii YIC ¼ loge 2 þ loge , (3) np i¼1 a^ 2i sy where s^ 2 is the sample variance of the model residuals; s2y is the sample variance of the measured system output about its mean value; np is the total number of model parameters, i.e. np ¼ n+m+1; a^ 2i is the square of the ith ^ and p^ ii is the ith diagonal element in the parameter vector a; element of the inverse cross product matrix P(N), so that s^ 2 p^ ii can be considered as an approximate estimate of the variance of the estimated uncertainty on the ith parameter estimate. The Young Identification Criterion, YIC, is a heuristic statistical criterion which consists of two terms. The first term provides a normalised measure of how well the model fits the data: the smaller the variance of the model residuals in relation to the variance of the measured output, the more negative this term becomes. The second term is a normalised measure of how well the model parameter estimates are defined. This term tends to become less negative when the model is overparameterised and the parameter estimates are poorly defined. Consequently, the model which minimises the YIC, provides a good compromise between goodness-of-fit and parametric efficiency. While the YIC can be a great help in ensuring that the model is not overparameterised, it is not always good at discriminating models that have a lower order than the ‘best’ model. Because of this, the YIC will often, if applied strictly, identify a model that is underparameterised. Therefore, it is used together with the coefficient of determination R2T , which is defined in Eq. (4): R2T ¼ 1  s2 . s2y (4) If the YIC identified model has an adequate R2T which is not significantly lower than the R2T of the higher order models, it may be fully accepted as the best model in statistical terms. In practical applications, of course, the use of the YIC and R2T will not guarantee that the ‘best’ model has been identified, because these statistics naturally depend upon the quality of the experimental time-series data. As a result, inadequate or very noisy data can lead to the identification of a model structure which may not be acceptable for some good physical reasons. In other words, mechanistic considerations are also important. 2.2.2. Mechanistic interpretation of the data-based models The basic differential equation for solute transport in a fluid, can be obtained in terms of ventilation rate and the volume of the WMZ. Under the assumption of a steadystate flow, with both the ventilation rate and the volume of the WMZ constant (Wallis et al., 1989), the mass conservation equation takes the form (Fig. 5): d ½V e xðtÞ ¼ Q eKt uðt  tÞ  QxðtÞ  K½V e xðtÞ, (5) dt where Q is the steady-state ventilation rate through the considered WMZ (m3/s); x(t) is the tracer gas concentration in the WMZ (l/m3); u(t) is the tracer gas concentration of the ventilated air (l/m3); t is the time delay between input and output (s); Ve is the volume of the WMZ (m3) and K is the decay rate coefficient (s1). The loss terms eKt and KVex(t) account for physical losses within the WMZ, such as leakage or decay of the tracer or for apparent losses such ARTICLE IN PRESS 336 A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 as poor mixing of the tracer between the input and the output concentration measurement points. Since CO2 is used as a tracer it is expected that the decay rate coefficient will be small. Next, a DBM model was used to describe and model the dynamics of the above system. When a set of usable input–output time-series data is generated, a reducedorder, linear model can be estimated to describe the data in a sufficiently accurate way. The continuous-time SRIV algorithm was used to identify the linear TF model (cf. Eq. (1)) between the supply air CO2 concentration (u(s)) and the CO2 concentration at the nine spatial points (x(s)) (Eq. (6)). Based on the results form the data-based phase, presented in Table 1, a first-order model showed to describe the result with high reliability and accuracy while using a minimal number of parameters. A first-order model was accepted since it does also provide a physical meaningful description of the mass dynamics: xðsÞ ¼ b0 ðets  eðtþdÞs ÞuðsÞ, s þ a1 where a1 ¼ K þ b0 ¼ Q Ve Q Kt e Ve ð7Þ The parameter d is the duration of the pulse of CO2 injection into the air flow over the helmet. So the physical derived model in the mechanistic phase of the DBM approach is based on the knowledge from the data-based phase that the underlying process should be first order. The amount of fresh air (volume (m3)) that enters a zone under the helmet per second (m3/s) is described by b0 (m3/ m3 s or s1). The amount of fresh air that enters a zone (m3) is physically different as the volume of the zone (m3). Therefore it is ambiguous to say that ventilation efficiency is simply expressed as s1. However, for the readability of this paper, we choose to express parameter b0 (Eq. (7)), the ventilation efficiency, in s1. (6) 2.2.3. The DBM model and classical heat transfer theory It is clear from the relationships between the parameters in the TF model (Eq. (6)) and the equivalent parameters in the estimated TF model (Eq. (7)), that not all the classical heat transfer coefficients are uniquely ‘identifiable’ from the experimental data. On the other hand, the heat transfer dynamics under the helmet are completely specified by the DBM parameters, which can be interpreted as specific combinations of these classical parameters. Consequently, this DBM model represents an alternative approach to modelling the system in physically meaningful, albeit not the normal, classical terms. Additional information about WMZ and the coupling between Data-Based Modelling and mechanistic interpretation can be found in Janssens et al. (2003), Van Brecht et al. (2005) and Zerihun Desta et al. (2005). K[Ve.x(t)] Q.e−K.τ.u(t−τ) u(t−τ) Ve.x(t) Q.x(t) WMZ Fig. 5. Schematic representation of the WMZ concept. Table 1 Average YIC and R2T values as a function of the sensor position and model structure [m, n, t] [0, 1, t] Position YIC R2T YIC R2T YIC R2T YIC R2T YIC R2T 10.12 10.08 9.229 9.054 9.386 9.660 9.575 8.923 10.72 0.975 0.974 0.964 0.958 0.955 0.968 0.965 0.961 0.982 10.31 8.614 7.899 5.846 8.920 9.909 8.318 9.817 9.511 0.992 0.995 0.988 0.955 0.960 0.981 0.978 0.996 0.997 7.044 6.761 7.430 7.421 8.164 7.938 7.364 9.437 5.671 0.992 0.995 0.996 0.988 0.993 0.991 0.993 0.998 0.996 10.54 11.63 11.65 9.312 9.559 10.72 10.54 10.02 10.46 0.995 0.995 0.995 0.983 0.980 0.993 0.989 0.990 0.992 9.209 8.751 6.387 4.911 7.835 7.449 7.419 9.248 7.939 1.000 0.998 0.997 0.989 0.992 0.995 0.995 0.997 0.999 9.639 0.967 8.794 0.982 7.470 0.994 10.49 0.990 7.683 0.996 1 2 3 4 5 6 7 8 9 Average [1, 2, t] [2, 3, t] [1, 1, t] [2, 2, t] ARTICLE IN PRESS A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 2.3. Experiments The helmet on the manikin human head was placed in an air flow generated by a fan that had a ventilation rate of 71500 m3/h. The fan was located 60 cm from the front of the dummy human head resulting in a mean air speed of 12 km/h. The generated air flow is not entirely pseudolaminar, but nevertheless it is a good approximation of realistic circumstances. Tracer gas experiments were carried out to quantify the ventilation characteristics under a helmet. For each of the nine positions (see Fig. 1), the tracer gas concentration was measured (using a sample rate of 0.33 Hz) in 10 repetitions as a result of a step in the tracer gas concentration of the ventilation air. The opening time of the injection of the pure CO2 gas was 10 s. 3. Results To calculate the ventilation characteristics with the DBM approach, first the experimental data are exploited to estimate the most appropriate model structure and associated model parameters and in the mechanistic phase, a model structure is formulated based on physical knowledge and assumptions about the physical nature of the process and in agreement with the model structure estimated in the data-based phase. 3.1. Model identification and estimation from the experimental data To identify and estimate a minimally parameterised continuous-time TF model between the supply air concentration as control input and the concentration at each of the nine spatially distributed sensor positions in the helmet, the continuous-time SRIV algorithm was run for first-, second- and third-order TF model structures, each time returning the parameter estimates with their associated relative standard error, the YIC value and the coefficient of determination R2T . To make a mechanistic interpretation viable, the order of the denumerator was limited to 3. This data-based identification procedure was applied to the identification experiments. The results are given in Table 1, where for all possible combinations, the best models in terms of the YIC and R2T value out of the 10 repetitions per sample position, are calculated by varying the time delay t. The model structures are defined by the number of numerator parameters, the number of denumerator parameters and the time delay. This is denoted as [m, n, t] (Eq. (2)). Based on the YIC value, the first-order models ([0, 1, t] and [1, 1, t]) yielded the highest score. This means that with a minimum of parameters, a good fit could be found ([0, 1, t]: R2T ¼ 0:967 and [1, 1, t]: R2T ¼ 0:990). The higher number of model parameters in the second ([1, 2, t] and [2, 2, t]) and third ([2, 3, t]) order models yielded a limited benefit in terms of the R2T value in comparison to the first- 337 order models and the uncertainty of the parameter estimates became higher. A model structure was chosen based on data-based identification and mechanistic interpretation, as explained in the materials and methods section. Therefore, the [1, 1, t] model is rejected, because the structure of this data-based model is not compatible with the structure of the mechanistic model as derived in TF model (Eq. (4)). Despite the strong YIC and good R2T values of the [1, 1, t] model, the first-order [0, 1, t] model is accepted based on data-based and mechanistic arguments, were the link between the estimated parameters and the physical meaning of the parameters is given in Eq. (6). As an example of the model fit, the different models for the tracer gas concentration and the residuals in time for position 6 are shown in Fig. 6. The resulting b0 parameters for the nine sampling points are shown in Table 2. These data-based parameters received their mechanistic interpretation from Eq. (6). 3.2. Quantification of the ventilation characteristics under a helmet An important variable to quantify the ventilation characteristics under a helmet is the ventilation efficiency through the WMZ. This is expressed in volume refreshments per second. From the pair of Eqs. (7), the ventilation efficiency (b0) and the decay rate coefficient (K) could be calculated for each of the nine sample positions under the helmet. As was expected, the decay rate coefficient was low (on average 0.014 s1) due to the use of CO2 as tracer gas. Fig. 7 shows the ventilations efficiency (b0) between head and helmet. Ventilation efficiency through the different WMZ ranged from 0.062 to 0.228 volume refreshments per second (s1). The average 95% confidence interval for the ventilation rate was 11.4% resulting in a confidence interval for the ventilation efficiency of 0.016 s1. These ventilation efficiencies were largest in the neighbourhood of the openings in the helmet (position 2: 0.19270.018 s1 and position 4: 0.22870.110 s1). The ventilation efficiency in the rear opening of the helmet at position 4 was larger then the ventilation efficiency in the front opening at position 2 since at the rear air is leaving the helmet which entered at other ventilation openings. The zones at the side of the helmet (ventilation efficiency position 8: 0.06270.002 s1 and position 9: 1 0.08570.004 s ) and fully at the rear side (position 5: 0.08570.007 s1) are badly ventilated. Position 8 has no ventilation opening, and therefore, the ventilation efficiency is very low. The ventilation opening at the side of the helmet is apparently very inefficient. Position 5, fully at the rear of the helmet is not much ventilated. Therefore, at these positions, one can expect thermal discomfort caused by high temperatures and high moisture concentrations when wearing a helmet during heavy cycling activity. In these circumstances, the general thermal comfort of the ARTICLE IN PRESS 338 A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 Fig. 6. Example of the different models and their residuals for the tracer gas concentration in time for position 6. Table 2 Average ventilation efficiency (s1) (b0 parameter from the data-based model) as a function of the sensor position Position Ventilation efficiency (s1), (bparameter) 1 2 3 4 5 6 7 8 9 0.140 0.192 0.158 0.228 0.085 0.168 0.132 0.062 0.085 helmet can be improved by increasing the flow of fresh air at these positions. 3.2.1. Effect of comfort angle To estimate the influence of the angle of inclination of a cyclist head on the ventilation under the helmet additional tests were performed. The head was tilted forward by 101 and by 301 (see Fig. 8b, 01 is a person standing straight and looking forward on a horizontal plane). A decathlon sports 900 helmet was used in an open wind tunnel producing a quasi-laminar flow (as described by De Bruyne et al., 2006). Air speed was set at 3 m/s (since most people cycle at low speed in daily life). The tracer gas concentration was measured (using a sample rate of 1 Hz) in three repetitions Fig. 7. Representation of the ventilation efficiency through the helmet (s1). as a result of a step in the tracer gas concentration of the ventilation air. The gas concentration was measured at nine positions on the head (see Fig. 8a) and under the helmet. Symmetry was assumed. Fig. 9 shows the relative change (%) in ventilation efficiency for nine positions [((Veff. 101–Veff. 301)/Veff. 101)  100]. An inclination angle of 101 was compared with ARTICLE IN PRESS A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 an angle of inclination of 301. Values above 0 show better ventilation effectiveness for an angle of inclination of 101. Box plots crossing 0 indicate that there was no significant variation between the two angles of inclination. (The lower and upper lines of the ‘box’ are the 5th and 95th percentiles of the sample.) The change in volume refreshment per second at the front of the helmet (position 1, 2, 6 and 7, see Fig. 9) was significant for position 2 (+23.3%, S.D. 19.8) and 6 (+22.1%, S.D. 8.9). Ventilation efficiency was better when the angle of inclination was set at 101 for these positions. 339 At the back of the helmet, the change in volume refreshment per second was significant for all positions (position 3: 82.8%, S.D. 31.8; position 4: 43.3%, S.D. 30.7; position 5: +35.9%, S.D. 7.9 and position 8: 36.6%, S.D. 13.0). However, ventilation efficiency was better for position 5 at an angle of inclination of 101, while position 3, 4 and 8 showed worse ventilation efficiency at an angle of inclination of 101. Ventilation at the side of helmet (position 9) was more than two times worse at an angle of inclination of 101 (244.4%, S.D. 60.3). Overall ventilation efficiency was worse when the angle of inclination was set at 101 (25.7%, S.D. 79.4). But this result was not significant and might be largely influenced by position 9 that has had very poor ventilation efficiency at an angle of inclination of 101. A non-uniform response to a changing angle of inclination can be explained by the changing orientation of the vents in the front of the helmet towards the flow. Brühwiler et al. (2006) showed that ventilation efficiency is, together with other factors, dependent on the vents at the front of the helmet. Changing angles of inclination will alter the effective vent opening perpendicular on the flow. 4. Discussion Fig. 8. (a) Position of tracer gas measurement. (b) Angle of inclination: 101 or 301. Ventilation efficiency is quantified using a tracer gas, giving information about the delay, time constants and ventilation efficiency (s1) of the air under the helmet. These responses were calculated for nine positions under the helmet. Information about local ventilation characteristics makes it possible to judge design alternatives for flow distribution under a helmet. Brühwiler et al. (2004, 2006) investigated the overall cooling power (J/s) of a helmet on the scalp or face. Liu and Holmer (1997) showed results of overall heat losses Fig. 9. Relative change (%) in ventilation efficiency for nine positions. ARTICLE IN PRESS 340 A. Van Brecht et al. / Applied Ergonomics 39 (2008) 332–341 (J/s) of a head for comparing ventilation effectiveness of a bicycle helmet. Liu and Holmer (1997), Brühwiler (2003) and Brühwiler et al. (2004, 2006) derived heat losses (J/s) using a heated and wetted manikin head in order to calculate the ventilation effectiveness of a helmet. Reid and Wang (2000) calculated the ventilation effectiveness as a function of the thermal conductance of a manikin head. Brühwiler et al. (2004) showed that the ventilation efficiency (J/s) of most helmets is improved when the head is tilted forward. Brühwiler et al. (2004) investigated 24 helmets and showed that cooling power ranged from 74.5 to 78 W at an air velocity of 1.67 m/s and from 78.5 to 714 W at an air velocity of 6.11 m/s. The helmets were investigated at an angle of inclination of 01 and 301. The influence of the inclination on the cooling power ranged from 71 to 70 W for 1.67 m/s and from 71 to 7+0.5 W for 6.11 m/s. Transferring these outcomes in relative percentages showed that the angle of inclination of 301 was up to 713% better as an angle of inclination of 101 at an air velocity of 6.11 m/s. At an air velocity of 1.67 m/s the angle of inclination of 301 was up to 718% better than an angle of 101. In our study, ventilation efficiency (s1) was largely dependent on the position under the helmet while Brühwiler et al. (2004, 2006) did only measure overall ventilation efficiency. Overall ventilation efficiency was also worse in our study at an angle of inclination of 101 compared to 301 (25.7%, S.D. 79.4). But these findings were not significant due to the large variations between the measurement positions. In our study, bad ventilation efficiency was seen at the side of the helmet (0.06 s1). This can be explained by the narrow air layer between head and helmet in this zone (70.5 cm), that will result in a poor flow rate (m3/s). Ventilation efficiency (0.22 s1) was optimal at the rear opening of the helmet. This can be caused by the design of the cushions under the helmet that form an air channel, enabling an air flow to the back of the helmet. The distance between head and helmet was 71.5 cm for the air channel in the middle of the helmet, making a strong flow rate (m3/s) possible. A heated manikin head that segregates water to simulate sensible and latent heat losses was used by Brühwiler (2003) and Brühwiler et al. (2006). Liu and Holmer (1997) showed a heated manikin head to simulate sensible heat losses. Tracer gas experiments presented in this paper were performed with non-heated manikin head that did not segregate water. Also the influence of hair and air velocity should be studied in further research. The influence of hair should not be underestimated, but the influence of heat losses on the convective flow should not be overestimated due to the air speed of 3 m/s. Only two bicycle helmets were used in this study: one to determine the ventilation characteristics under a helmet and one to look for the influence of the inclination angle. In the future, more helmets have to be investigated to compare different helmet ventilation designs. This research outlines the method of using tracer gas to quantify ventilation efficiency under a helmet. Thermal discomfort is a barrier for helmet use. Reid and Wang (2000) and Ellis et al. (2000) suggested that placing more holes in helmet does not necessary increase thermal comfort, while the helmets provide less damping in a crash. The suggested method allows judging the usefulness of individual vents and air channels under the helmet. Fewer ventilation holes that are carefully positioned and ventilation channels within the helmet could optimise thermal and mechanical requirements simultaneously. 5. Conclusions Ventilation efficiency was described using tracer gas concentration of ventilated air. A compact first-order model proved to describe the results with high accuracy while it allowed mechanistic interpretation. The method is useful to investigate ventilation characteristics of different types of helmets. Local ventilation characteristics are given, providing information to optimise air flow under a helmet. Using this approach, ventilation efficiencies ranging from 0.06 s1 at the side of the helmet to 0.22 s1 at the rear vent were found. The zones at the side of the helmet (position 8: 0.06270.002 s1 and position 9: 0.08570.004 s1) and fully at the rear side (position 5: 0.08570.007 s1) are badly ventilated. General comfort of the investigated helmet can be improved by increasing the ventilation efficiency at these problem zones. The angle of inclination was also found to influence the ventilation efficiency, although the results were largely depending upon the position under the helmet. Ventilation efficiency was significantly better at a low angle of inclination (101 compared to 301) for position 2 (+23.3%, S.D. 19.8), and 6 (+22.1%, S.D. 8.9) at the front of the helmet and for position 5 (+35.9%, S.D. 7.9) at the rear of the helmet. Ventilation efficiency was significantly worse at a low angle of inclination for position 3 (82.8%, S.D. 31.8), position 4 (43.3%, S.D. 30.7) and position 8 (36.6%, S.D. 13.0) at the rear of the helmet. Position 9 at the side of the helmet showed a relative poor ventilation effectiveness for the low angle of inclination (244.4%, S.D. 60.3). Overall ventilation efficiency was worse when the angle of inclination was set at 101 (25.7%, S.D. 79.4). 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